I'm wondering what benefits there is to using "bridged" mode on a modem. If your router can handle PPPoE, is there any reason to bridge it over to the router, rather than having it run on the modem?
I normally keep running PPPoE on the modem to ensure a tiny bit lesser load on my router and let the modem do the job it was specifically optimized to do best. However, I sometimes switch it to the modem for two reasons:
In my case the modem's lights are hiding or set off to one side. Even when they're in front of me, it is harder to know that PPP is temporarily down because the modem just turns off one green indicator in a row of 4 or 5 other equal green indicators.
Spiff is correct...
If the DSL modem handles the PPPoE connection, then the modem will distribute private, non-public internet IP addresses to the device / devices connected to its ethernet port with incoming traffic from the internet. The process of moving between public (internet) and private (internal network) IP addresses is called Network Address Translation (NAT). NAT can also be considered a firewall of sorts because it masks the internal IP's / individual computers.
Depending on how many IP addresses the DHCP server on the modem handles, you could technically connect a switch to the ethernet port and the modem will hand out private IP addresses to the devices that are connected and you wouldn't need a router.
If you would like to have a router to provide more control like a better firewall, wireless, and possibly more devices connected, then you would opt for a wired / wireless router.
By default, a router would acquire an IP address from the modem (private or public) and would perform NAT and isolate the devices from the "outside network". If the modem is handling the PPPoE, then the router would receive a private IP from the modem and then create another private network via NAT. There would be two layers of private networks in this instance and is recognized by many devices as "Double NAT" which may cause issues with traffic trying to find its way in and out of your network and possibly increase latency.
There are two ways you can mitigate this issue:
Whichever device does PPPoE also has to do NAT, and whichever device does NAT usually does DHCP. If your router has a better, more flexible NAT and a better DHCP server, let your router do it.
You don't want both devices doing NAT if you can avoid it. That's called "double NAT" and tends to cause problems for people who don't know what they're doing (and even some who do).